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3 years ago

What is the area of the figure?

Mathematics

1 answer:

Stolb23 [73]3 years ago

7 0

<span>What is the area of the figure?The area of the figure is 1180cm</span>

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Let X be a continuous random variable with density functionf(x)={1−|x|0 for −1

BlackZzzverrR [31]

Answer:

$f_Y (y) =\frac{d}{dy} = 2 \frac{1}{2 |\sqrt{y}|} -1 = \frac{1}{|\sqrt{y}|} -1,0 \leq Y\leq 1$

Step-by-step explanation:

For this case we want to find the density function for $Y=X^2$

And we have the following density function for the random variable X:

$f(X) = 1- |X|,-1 \leq X \leq 1$

So we can do this replacing $Y=X^2$

$F_Y (Y \leq y) = P(X^2 \leq y)$

If we apply square root on both sides we got:

$P(-\sqrt{y} \leq X \leq \sqrt{y}) = \int_{-\sqrt{y}}^0 1+t dt +\int_{0}^{\sqrt{y}} 1-t dt$

And if we integrate we got this:

$F_Y (y) = [t+ \frac{t^2}{2}] \Big|_{-\sqrt{y}}^0+ [t -\frac{t^2}{2}] \Big|_{0}^{\sqrt{y}}$

And replacing we got:

$F_Y (y) = [0 -(-\sqrt{y} +\frac{y}{2})] + [\sqrt{y} -\frac{y}{2}]$

$F_Y (y) = 2 |\sqrt{y}| -y$

And if we want to find the density function we just need to derivate the pdf like this:

$f_Y (y) =\frac{d}{dy} = 2 \frac{1}{2 |\sqrt{y}|} -1 = \frac{1}{|\sqrt{y}|} -1,0 \leq Y\leq 1$

3 0

4 years ago

ABCD is a trapezium with AB= x cm, DC=( x+ 4 )cm and the distance between the parallel sides AB and DC is 1/2 x cm

horsena [70]

We know that the smaller base is x cm, the greater base is x+4 cm, and that the height is x/2 cm.

Since the area of a trapezium is given by

$A=\dfrac{(b+B)h}{2}$

If we plug the expressions we have

$A=\dfrac{(x+(x+4))\frac{x}{2}}{2}=\dfrac{(2x+4)x}{4}=\dfrac{2x^2+4x}{4}$

If this must equal 84, we can solve for x as follows: start with

$\dfrac{2x^2+4x}{4}=84$

Multiply both sides by 4:

$2x^2+4x=336$

Subtract 336 from both sides:

$2x^2+4x-336=0$

We can divide both sides by 2 to make computation simpler:

$x^2+2x-168=0$

Use the quadratic formula (or any mean you prefer) to solve this equation and get the solutions

$x_1=-14,\quad x_2=12$

We can't accept the negative solution, because it would imply

$AB=-14,\quad CD=-10$

and we can't have negative side lengths. So, the answer is 12.

4 0

3 years ago

I need help please?!!!!!

igor_vitrenko [27]

Answer:

Tax=6%

So original price=100%

New price =100%+6%=106%

10.5*(106/100)=

10.5*1.06=11.13

55*1.06= 58.3

58.3-11.13= 47.17

The difference is 47 dollars

$47

4 0

3 years ago

The sales tax on a $350 computer is $ 22.75. find the sales tax rate.

likoan [24]

Set up an equation to solve for the tax rate, x:

$350(x) = 22.75\\x = \frac{22.75}{350}\\x = 0.065\\x = 6.5%$

We can conclude that the tax rate on the computer was 6.5 percent.

7 0

3 years ago

Liam bought a picture frame that cost $12 plus 8% sales tax. He wrote the expression 1.08(12) to find his total cost.

AnnyKZ [126]

Answer:

Step-by-step explanation:

hope this helps!! :)

6 0

3 years ago

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